At any instant the velocity of a particle of mass 500 g is 2 t i ^ + 3 t 2 j ^ m s - 1 . If the force acting on the particle at t = 1 s is ( i ^ + x j ^ ) N . Then the value of x will be:

Step-by-step solution

The equation for velocity is v → = 2 t   i ^   +   3 t 2   j ^ Thus, the acceleration is a → = d v → d t = d ( 2 t   i ^ + 3 t 2   j ^ ) d t = 2   i ^ + 6 t   j ^ At t = 1   s , a → = 2   i ^   +   6   j ^ The force is written as F → = m a → = 2   i ^ + 6   j ^ 2 = i ^   + 3   j ^ Comparing it with the given value of force, x = 3 .